Simplify: frac{3+sqrt{6}}{17 sqrt{3}-2 sqrt{3 | vedclass

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(C) Given expression: $\frac{3+\sqrt{6}}{17 \sqrt{3}-2 \sqrt{32}+3 \sqrt{18}-4 \sqrt{48}}$Simplify the denominator terms:$2 \sqrt{32} = 2 \sqrt{16 	i

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$\sqrt{3}$

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(C) Given expression: $\frac{3+\sqrt{6}}{17 \sqrt{3}-2 \sqrt{32}+3 \sqrt{18}-4 \sqrt{48}}$Simplify the denominator terms:$2 \sqrt{32} = 2 \sqrt{16 	imes 2} = 2 	imes 4 \sqrt{2} = 8 \sqrt{2}$$3 \sqrt{18} = 3 \sqrt{9 	imes 2} = 3 	imes 3 \sqrt{2} = 9 \sqrt{2}$$4 \sqrt{48} = 4 \sqrt{16 	imes 3} = 4 	imes 4 \sqrt{3} = 16 \sqrt{3}$Substitute these back into the denominator:$17 \sqrt{3} - 8 \sqrt{2} + 9 \sqrt{2} - 16 \sqrt{3}$Group like terms:$(17 \sqrt{3} - 16 \sqrt{3}) + (9 \sqrt{2} - 8 \sqrt{2}) = \sqrt{3} + \sqrt{2}$Now the expression becomes: $\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}$Factor the numerator: $3 + \sqrt{6} = \sqrt{3} 	imes \sqrt{3} + \sqrt{3} 	imes \sqrt{2} = \sqrt{3}(\sqrt{3} + \sqrt{2})$Substitute back: $\frac{\sqrt{3}(\sqrt{3} + \sqrt{2})}{\sqrt{3} + \sqrt{2}} = \sqrt{3}$

Simplify: $\frac{3+\sqrt{6}}{17 \sqrt{3}-2 \sqrt{32}+3 \sqrt{18}-4 \sqrt{48}}$

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